In recent years, all the operating principles of intermediate band behaviour have been demonstrated in InAs/GaAs quantum dot (QD) solar cells. Having passed this hurdle, a new stage of research is underway, whose goal is to deliver QD solar cells with efficiencies above those of state-of-the-art single-gap devices. In this work, we demonstrate that this is possible, using the present InAs/GaAs QD system, if the QDs are made to be radiatively dominated, and if absorption enhancements are achieved by a combination of increasing the number of QDs and light trapping. A quantitative prediction is also made of the absorption enhancements required, suggesting that a 30 fold increase in the number of QDs and a light trapping enhancement of 10 are sufficient. Finally, insight is given into the relative merits of absorption enhancement via increasing QD numbers and via light trapping. (C) 2014 Elsevier B.V. All rights reserved.